Galactic Nuclei

A&A manuscript no. (will be inserted by hand later) Your thesaurus codes are: 06 (02.01.3; 02.01.4; 02.12.1; 03.20.8; 11.01.2; 11.17.2; 13.25.2)

ASTRONOMY AND ASTROPHYSICS

X-ray photoionized plasma diagnostics with Helium-like ions. Application to Warm Absorber-Emitter in Active Galactic Nuclei.

arXiv:astro-ph/0002319v1 16 Feb 2000

Delphine Porquet1,2 & Jacques Dubau3 1 2 3

DAEC, Observatoire de Paris, Section Meudon, F-92195 Meudon Cedex, France CEA/DSM/DAPNIA, Service d’Astrophysique, CEA Saclay, F-91191 Gif sur Yvette Cedex, France DARC, Observatoire de Paris, Section Meudon, F-92195 Meudon Cedex, France

Received ...; accepted ...

Abstract. We present He-like line ratios (resonance, intercombination and forbidden lines) for totally and partially photoionized media. For solar plasmas, these line ratios are already widely used for density and temperature diagnostics of coronal (collisional) plasmas. In the case of totally and partially photoionized plasmas, He-like line ratios allow for the determination of the ionization processes involved in the plasma (photoionization with or without an additional collisional ionization process), as well as the density and the electronic temperature. With the new generation of X-ray satellites, Chandra / AXAF, XMM and Astro-E, it will be feasible to obtain both high spectral resolution and high sensitivity observations. Thus in the coming years, the ratios of these three components will be measurable for a large number of non-solar objects. In particular, these ratios could be applied to the Warm Absorber-Emitter, commonly present in Active Galactic Nuclei (AGN). A better understanding of the Warm Absorber connection to other regions (Broad Line Region, Narrow Line Region) in AGN (Seyferts type-1 and type-2, low- and high-redshift quasars...) will be an important key to obtaining strong constraints on unified schemes. We have calculated He-like line ratios, for Z=6, 7, 8, 10, 12 and 14, taking into account the upper level radiative cascades which we have computed for radiative and dielectronic recombinations and collisional excitation. The atomic data are tabulated over a wide range of temperatures in order to be used for interpreting a large variety of astrophysical plasmas.

Key words: Atomic data – Atomic process – Techniques: spectroscopic – Galaxies: Active – (Galaxies:) quasars: emission lines – X-rays: galaxies

Send offprint requests to: D. Porquet Correspondence to: [email protected]

1. Introduction The new X-ray satellites (Chandra, XMM and Astro-E) will offer unprecedented high spectral resolution and high sensitivity spectra. Indeed, it will be possible to observe and to separate, in the X-ray range, the three most intense lines of He-like ions: the resonance line (w: 1s2 1 S 0 – 1s2p 1 P 1 ), the intercombination lines (x,y: 1s2 1 S 0 – 1s2p 3 P 2,1 respectively) and the forbidden line (z: 1s2 1 S 0 – 1s2s 3 S 1 ). They correspond to transitions between the n=2 shell and the n=1 ground state shell (see Figure 1). The ratios of these lines are already widely used for collisional (coronal) plasma diagnostics of various types of objects: solar flares, supernovae remnants, the interstellar medium and tokamak plasmas, i.e. for very hot collisional plasmas (Mewe & Schrijver 1978a 1978b, Winkler et al. 1981, Doyle & Schwob 1982, and Pradhan & Shull 1981). As shown by Gabriel & Jordan (1969, 1972, 1973), these ratios are sensitive to electron density (R(ne ), equation 1) and to electronic temperature (G(Te ), equation 2): z (1) R (ne ) = (x + y) G (Te ) =

z + (x + y) w

(2)

As emphasized by Pradhan (1985), Liedahl (1999) and Mewe (1999) (see also Paerels et al. 1998), these plasma diagnostics could be also extended to study photoionized plasmas. Indeed, Pradhan has calculated the R and G ratios for highly charged ions (Ar xvii and Fe xxv) in “recombination dominated non-coronal plasmas”. We present numerical calculations of these ratios, for six lighter ions, which could be applied directly for the first time to Chandra and XMM observations of the Warm Absorber present in Active Galactic Nuclei (AGN), and especially in Seyfert 1. The Warm Absorber (WA) is a totally or a partially photoionized medium (with or without an additional

2

Porquet & Dubau: Photoionized plasma diagnostics with He-like ions

ionization process), first proposed by Halpern (1984) in order to explain the shape of the X-ray spectrum of the QSO MR2251-178, observed with the Einstein Observatory. Its main signatures are the two high-ionization oxygen absorption edges, O vii and O viii at 0.74 keV and 0.87 keV respectively, seen in fifty percent of Seyfert 1 galaxies at least (Nandra & Pounds 1994, Reynolds 1997, George et al. 1998). According to Netzer (1993), an emission line spectrum from the WA should also be observed. Indeed, He-like ion lines have been observed in different types of Seyfert galaxies (NGC 3783: George et al. 1995, MCG-6-30-15: Otani et al. 1996, E 1615+061: Piro et al. 1997, NGC 4151: Leighly et al. 1997, NGC 1068: Ueno et al. 1994, Netzer & Turner 1997, and Iwasawa et al. 1997). The WA is supposed to be at least a two-zone medium with an inner part (called the “inner WA”) associated with O viii and an outer part (called the “outer WA”), less ionized, associated with O vii (Reynolds 1997, Porquet et al. 1999). Furthermore, the O vii line is predicted to be the strongest line associated with the outer WA; the Ne ix line is predicted to be one of the strongest lines formed in the inner WA (Porquet et al. 1998). The ionization processes, that occur in the Warm Absorber, are still not very well known. Indeed, even though the WA is commonly thought to be a photoionized gas, an additional ionization process cannot be ruled out (Porquet & Dumont 1998, Porquet et al. 1999, Nicastro et al. 1999). Thus, in the present paper, we do not restrict ourselves to only a single type of plasma, but rather study the following cases. We consider a “pure photoionized plasma” to be a plasma ionized by high energy photons (external ionizing source). For such a plasma, H-like radiative recombination (and dielectronic recombination at high temperature) are dominant compared to electronic excitation from the ground level (1s2 ) of He-like ions. The lines are formed by recombination. A “hybrid plasma” is a partially photoionized plasma, but with an additional ionization process, e.g. collisional (internal ionizing source). For this case, He-like electronic excitation processes from the ground level are usually as important as H-like recombinations, and may even dominate. The lines are formed by collisional excitation from the ground level with or without recombination. In the next section, we introduce the atomic data calculations needed for such plasmas and we emphasize the role of upper-level radiative cascade contributions calculated in this paper for the populations of the n=2 shell levels. In section 3, we develop line diagnostics of the ionization process (temperature) and the density for pure photoionized and hybrid plasmas. We give the corresponding numerical calculations of the line ratios for C v, N vi, O vii, Ne ix, Mg xi, and Si xiii. In section 4, we give a practical method for using these results to determine the

physical parameters of the WA, in the context of the expected data from the new X-ray satellites (section 5).

2. Atomic data Liedahl (1999) described the basic mechanisms of density diagnostics for X-ray photoionized plasmas from He-like ions. As he noted, a proper calculation of the population of the n=2 shell levels depends upon a number of additional levels. We propose in this article to use extensive calculations of atomic data taking into account upper level (n>2) radiative cascade contribution on n=2 shell levels for C v, N vi, O vii, Ne ix, Mg xi, and Si xiii, to give a much more precise treatment of this plasma diagnostic. We consider in this paper, the main atomic processes involved in pure photoionized and hybrid plasmas: radiative recombination and dielectronic recombination (only important for high temperature plasmas), collisional excitation inside the n=2 shell, and collisional excitation from the ground level (important for high temperature plasmas). 2.1. Energy levels, radiative transition probabilities Using the SUPERSTRUCTURE code (Eissner et al. 1974), we have calculated the energy levels for the first 49 fine-structure levels (2S+1 LJ ) for the six ions. This corresponds to the levels of the first 15 configurations (from 1s2 to 1s5g). Nevertheless, for the first seven levels, we have preferred to use the Vainshtein & Safronova (1985) data which have a slightly better accuracy (∼10−3 ). In Table 1, in order to reduce the amount of data, we only report the energy levels for the first 17 levels (n=1 to n=3 shell). The values for the others levels are available on request. The transition probabilities (Aki in s−1 ) for the “allowed” transition (E1), are also calculated by the SUPERSTRUCTURE code; for the other transitions (M1, M2 & 2E1) the Aki values are from Lin et al. (1977). In a same way, only direct radiative contributions of the first 17 levels onto the first 7 levels are given in Table 2.

2.2. Recombination coefficient rates Blumenthal et al. (1972) have noted that radiative and dielectronic recombination can have a significant effect on the populations of the n=2 states in He-like ions through radiative cascades from higher levels as well as through direct recombination. 2.2.1. Radiative recombination (RR) coefficients rates For radiative recombination rate coefficients, we have used the method of Bely-Dubau et al. (1982a). This method is based on (Z − 0.5) screened hydrogenic approximation of


the Burgess (1958) formulae, as we explain below. For recombination of a bare nucleus of charge Z to form H-like ions, Burgess (1958) fitted simple power law expressions to the “exact” theoretical hydrogenic photoionization cross-sections σnl (E) (in cm2 ) for the nl levels (1 ≤ n ≤ 12 and 0 ≤ l ≤ n − 1). According to Burgess “for moderately small n, the errors should be not more than about 5%. Such accuracy should be sufficient for most astrophysical applications”. 1 Z2 σnl (E) = 0.55597 2 n 2(2l + 1) " γ(nl,l−1) IH Z 2 × l |σ(nl, o l − 1)|2 n2 E # 2 γ(nl,l+1) I Z H (3) + (l + 1) |σ(nl, o l + 1)|2 n2 E where E is the photon energy E ≥ IH Z 2 /n2 . Bely-Dubau et al. (1982a) used this equation for He-like 1snl levels by replacing Z with (Z − 0.5). The quantity (Z − 0.5) was chosen to take into account the screening of the 1s orbital. To check the validity of this assumption we compared the photoionization cross sections obtained from equation (3) to the recent calculations of the Opacity Project by Fernley et al. (1987). In Figure 2 are plotted photoionisation cross sections for 1s2s 1 S 3 S, 1s2p 1 P 3 P and 1s10d 1 D 3 D for Z =6, 10, 14 (continuous curves), scaled as (Z − 0.5). With the exception of 1s2p 1 P, the three continuous curves can hardly be distinguished. Furthermore, the curves do not differ when passing from singlet to triplet cases. This is strong evidence that for 1snl, it is possible to use screened hydrogenic calculations. For comparison, we give the present calculation corresponding to formulae (3) modified (empty circles). The Opacity Project data were taken from the Topbase Bank (Cunto et al. 1993). This bank includes the 1snl photoionization cross sections for 1 ≤ n ≤ 10 and l = 0, 1, 2. The Burgess data, σ(nl, o l ± 1) and γ(nl, l ± 1), are more complete since they also include 3 ≤ l ≤ n − 1. Formula (3) is also more convenient since being analytic one can derive directly the radiative recombination rates (cm3 s−1 ) from it. αnl (Z, Te ) = 8.9671 × 10−23 T3/2 Z fnl (Te ) e

(4)

where Te is the electronic temperature, Z is the atomic number and x3n [ l|σ(nl, o l − 1)|2 Γc (xn , 3 − γ(nl, l − 1)) n2 +(l + 1) |σ(nl, o l + 1)|2 Γc (xn , 3 − γ(nl, l + 1))] (5) Z 2 IH IH with xn = = 157 890 (6) 2 k k Te n fnl (Te ) =

3

The quantities |σ(nl, o l ± 1)|/n2 and γ(nl, l ± 1) are given in Table I of Burgess and Z ∞ ex t(p−1) e−t dt (7) Γc (x, p) = p x x Finally, to transform H-like data to He-like data, we used the two following expressions for 1s2 and 1s nl: α1s2 = α1s

1 α1s (Z, Te ) (n = 1, ground level) 2

nl (LSJ)

=

(8)

(2J + 1) αnl (Z, Te ) (n ≥ 2) (2L + 1) (2S + 1)

(9)

And we replace Z by (Z-0.5) in formula (4) and (6). For 102 levels on each 1s2l level (1s 2s 3 S1 , 1 S0 ; 1s 2p 3 P0 , 3 P1 , 3 P2 , 1 P1 ; n=2 shell levels). The present study has shown that the radiative recombination (RR) is slowly convergent with n, thus the first 49 levels (n≤5) are considered as fine-structure levels (LSJ), the levels from n=6 to n=10 (l=9) shells are separated in LS term (Bely-Dubau et al. 1982a, 1982b), and finally levels from n=11 to n=∞ are taken into account inside n=10. Figure 3 shows the scaled direct plus upper (n>2) level radiative cascade RR rates αs =T1/2 α/(Z-0.5)2 versus Ts =T/(Z-0.5)2 for 1s2l levels (Z= 8, 10, 12 and 14), and for comparison the direct RR contribution. T is in Kelvin. This points out the importance of the cascade contribution at low temperature. The αs curves are very well superposed and thus allows us to deduce the RR rate coefficients for other Z, as for example Z = 9,11,13. Tables 4, 5, 6, 7 and 8 report separately the direct and the cascade contribution to the RR rate coefficients for

4


each 1s2l level. We checked that the calculated rates summed over n ≥ 2 and l, added to the rate of the 1s2 (ground level) level, are similar to the total RR rates calculated by Arnaud & Rothenflug (1985), Pequignot et al. (1991), Mazzotta et al. (1998), Jacobs et al. (1977) (for He-like Fe ion) and Nahar (1999) (for O vii). Since these authors used hydrogenic formulae, the RR rate coefficient depends on which screening value was used. As already noted, we have taken for our calculations a screening of 0.5 which is a realistic screening of the atomic nuclei by the 1s inner electron. Most probably, some of these authors have used a (Z-1) scaling. For example for C v, a screening of unity implies a lower value by some 20% with respect to the value obtained with a screening of 0.5.

2.2.2. Dielectronic recombination (DR) coefficient rates For the low temperature range (photoionized plasma) considered in this paper the dielectronic recombination can be neglected. However at high temperatures, the contribution of DR is no longer negligible. Therefore, we have calculated DR coefficients rates (direct plus upper (n >2) level radiative cascade contribution). We used the same method as Bely-Dubau et al. (1982a). The AUTOLSJ code (including the SUPERSTRUCTURE code) was run with 42 configurations belonging to 1snl, 2snl and 2pnl, with n ≤ 5. All the fine-structure radiative and autoionization probabilities were calculated. For low Z ions, it was necessary to do an extrapolation to higher n autoionizing levels. Specifically, we extrapolate autoionization probabilities, as 1/n3 , while keeping the radiative probabilities constant. This extrapolation is not perfectly accurate, and we can estimate that the RD for C, N and O might be slightly over or under estimated. In Table 4 ,5, 6, 7, and 8, the DR rates are reported for Z=6, 8, 10, 12, 14 over a wide range of temperature.

2.3. Electron excitation rate coefficients The collisional excitation (CE) rate coefficient (in cm3 s−1 ) for each transition is given by: ∆Eij 8.60 × 10−6 Υij (Te ) exp − Cij (Te ) = kT gi T1/2

(15)

Where ∆Eij is the energy of the transition, gi is the statistical weight of the lower level of the transition, and Υij is the so-called effective collision strength of the transition i→j.

The 1s 2l–1s 2l′ transitions (i.e. inside the n=2 shell) are very important for density diagnostic purpose. The data are from Zhang & Sampson (1987). Below, we report scaled effective collision strength Υsij =(Z-0.5)2 Υij . We also use a scaled electronic temperature Ts = T(K)/(1000 Z 2 ). The (Z-0.5)2 coefficient has been chosen to obtain scaled Υs almost independent of Z (for 6 ≤ Z ≤ 14). In Figure 4, Υs (Ts ) is displayed for the four most important transitions (between 23 S1 and 23 P0,1,2 levels, and between 21 S0 and 21 P1 levels) including both direct and resonant contribution, and for comparison the direct contribution alone is shown for Z=8. We remark that the curves Υs (Ts ) are nearly identical for different Z, and for these transitions the resonant contribution is quite negligible since the two curves for Z=8 are superposed. The rates for the transitions between 23 S1 and 23 P0,1,2 levels are proportional to their statistical weight. The curves for transitions 23 S1 –23 P1 21 S0 –21 P1 are nearly identical. These high values of Υs inside the n=2 shell and the small energy difference between these levels, favour transitions by excitation between the n=2 shell levels. Thus the excitation inside the n=2 shell should be taken into account even for low temperature plasmas. Excitation from n=2 levels to higher shell levels can be neglected due to the weak population of the n=2 shell compared to the ground level (n=1) in a moderate density plasma and also due to the high Υs (Ts ) values inside the n=2 shell which favour transitions between the n=2 levels, as we see below. CE from the 1s2 (ground) level to excited levels are only important for high temperature such as the hybrid case, due to the high energy difference between these levels. For 1s2 –1s2l transitions, we have used the effective collision strength values from Zhang & Sampson (1987). These values include both non-resonant and resonant contributions. CE rates for the 1s2 –1snl (3≤n≤5) transitions are from Sampson et al. (1983). Their calculations do not include resonance effects but these are expected to be relatively small (Dubau 1994). The rates converge as n−3 . We have calculated the radiative cascade contribution from n>2 levels for each n=2 level. We have considered the first 49 levels, as fine-structure levels (LSJ); the contributions from the n=6 to n=∞ levels are considered to converge as n−3 . The cascade contributions become more important for high temperatures. The cascade contribution (from n >2 levels) increases steadily with temperature and has an effect mostly on the 1s 2s3 S1 level. The resonant contribution increases then decreases with temperature. For high temperature plasmas, cascade effects should be taken into account. For very low temperature plasmas only the direct non-resonant contribution is important, except for the 1s 2s 3 S1 level which also receives cascade from within the n=2 level, i.e. from 1s 2p 3 P0,1,2


levels, as long as the density does not redistribute the level population, i.e. the density is not above the critical density. Tables 9, 10, 11, 12 and 13 report data which correspond respectively to the direct (b), the resonance (c), and the n >2 cascade (d) contributions. 3. Plasma diagnostics 3.1. Computation of the line ratios The intensities of the three component lines (resonance, forbidden and intercombination) are calculated from atomic data presented in the former section. The ratios R(ne ) and G(Te ) are calculated for C v, N vi, O vii, Ne ix, Mg xi, and Si xiii. The wavelengths of these three lines for each He-like ion treated in this paper are reported in Table 14. We note that for all temperatures (low and high), we have included in the line ratio calculations, RR contribution (direct + upper-level radiative cascade), and collisional excitations inside the n=2 shell. For high temperature plasmas, the CE contribution (direct + resonance + cascade) from the ground level (n=1 shell, 1s2 ) should be included in the calculations as well as DR (direct + cascade). Figure 5 displays these different contributions which populate a given n=2 level. As emphasized previously, the cascade contribution from n>2 levels, especially for the 3 S1 level, should be taken into account in line ratio calculations since this level is responsible for the forbidden component (z) line, which appears in both ratios R and G. For a pure photoionized plasma, when no upper level radiative cascade contribution is included in the RR rates, R and G could be underestimated by 6–10% (for O vii). In a hybrid plasma, where collisional processes from the ground level are not negligible, the ratio R is lower by ∼20% at T=3.6 106 K, when no cascades from upper levels are taken into account. In a similar way, the value of G would be underestimated. We also point out the importance of taking into account the branching ratios in the calculations of x and y lines. Bx = A5→1 / (A5→1 + A5→2 ), and By = A4→1 / (A4→1 + A4→2 ) are respectively the branching ratios of the x and y lines (Aj→i being the transition probability from level j to level i, see Fig. 1). Branching ratios are very important in the case of light nuclear charge (Z), as shown in Figure 6, for C v, A5→1 2 level (He-like)

(4’) (2’) an n=2 level (He-like)

(2) (1)

ground level (n=1, 1s2) (He-like)

Fig. 5. Simplified Gotrian diagram reporting the different contributions for the population of a given n=2 shell level. (1): direct contribution due to collisional excitation (CE) from the ground level (1s2 ) of He-like ions; (2)+(2’): CE upper level radiative cascade contribution; (3): direct RR or direct DR from H-like ions contribution; and (4)+(4’): RR or DR upper level radiative cascade contribution. Note: CE and DR are only effective at high temperature.

12


CV

Si XIII

5

5

4

4

5.73(+07)

1.98(+08) 3

3

1.61(+08)

5.65(+07)

1.47(+08)

5.62(+07)

2

2

3.89(+07)

2.16(+07) 2.65(+04)

3.61(+05)

4.96(+01) 1

1.35(+11)

1

Fig. 6. Simplified Gotrian diagrams for C v and Si xiii. Thick curves correspond to the strongest radiative transitions (Ai→j in s−1 ), and thin curves correspond to lower values.

Porquet & Dubau: Photoionized plasma diagnostics with He-like ions 5.0 4.5

5.0

CV

4.5

4.0

4.0

3.5

3.5

3.0

G

Ne IX

3.0

G

2.5 2.0

+4

1.5

+3

photoionized

hybrid

1.0

+2 +1 0

0.5 0.0

10

5

10

2.5 2.0

+4 +3

1.5

+2

1.0

+1 0

0.5 collisional

6

10

−1

0.0 5 10

7

6

5.0

N VI

4.5

4.5

4.0

4.0

3.5

3.5

Mg XI

3.0

G

2.5

+4 +3

2.0 1.5

2.5

+3

2.0

+2

1.5

+2 +1 0

1.0 0.5 0.0

5

1.0

0.0 5 10

6

10

+1 0 −1

0.5

10

Te (K) 5.0 4.5

10

Te (K)

3.0

G

7

10

Te (K) 5.0

13

10

6

10

7

Te (K) 5.0

O VII

Si XIII

4.0

4.0

3.5 3.0

G

3.0

2.5

+2

+4 +3

2.0 1.5

2.0

+2

1.0

5

10

6

10

Te (K)

+1

1.0

+1 0 −1

0.5 0.0

+3

G

7

10

0.0 5 10

0 −1 −2 10

6

10

7

Te (K)

Fig. 7. G (=(x+y+z)/w) is reported as a function of electronic temperature (Te ) for C v, N vi, O vii, Ne ix, Mg xi, and Si xiii in the density range where G is not dependent on density (see §3.2). The number (m) associated to each curves means Xion =10m, where Xion is the ratio of H-like ions over He-like ions. As an example for Oxygen (Z=8) it corresponds to ratio of the relative ionic abundance of O viii/O vii ground state population.

14

Porquet & Dubau: Photoionized plasma diagnostics with He-like ions 16

4.0

CV 14

3.5

12

3.0

10

R

Ne IX

2.5

R

8

2.0 4

6

T= 7 10 K

5

T =2 10 K

1.5

5

5

T= 1.5 10 K

4

T= 7 10 K

1.0

5

T= 4 10 K

6

T= 2 10 K

6

0 5 10

6

T= 1.5 10 K

2

T= 5.6 10 K

0.5

10

6

10

7

10

8

10

9

10

−3

10

10

11

10

0.0 8 10

12

9

10

10

11

10

10

ne (cm )

12

10 −3

13

10

14

10

15

10

ne ( cm )

7

3.5

N VI

6

Mg XI

3.0 5

2.5 4

R 2.0

R 3

1.5

5

T= 3 10 K

4

T= 8 10 K

2

6

5

T= 2 10 K

T= 10 K

1.0

6

T= 3.2 10 K

5

T= 6.3 10 K

1 0 6 10

6

6

T= 2 10 K

7

10

T= 8 10 K

0.5

8

9

10

10

10

11

10

12

10

−3

10

0.0 9 10

13

10

10

10

11

12

10

10

13

10 −3

14

10

15

10

16

10

ne (cm )

ne (cm ) 5

3.0

O VII 4

2.5 2.0

3

R

R 2

1.5 5

5

T= 4 10 K

T= 10 K

1.0

5

T= 5 10 K

T= 5 10 K

T= 10 K

1

6

0.5

T= 1.8 10 K

7

10

8

10

6

T= 1.6 10 K 6

6

0 6 10

Si XIII

9

10

10

10

−3

11

10

ne (cm )

12

10

13

10

14

10

7

T= 10 K

0.0 9 10 11 12 13 14 15 16 17 10 10 10 10 10 10 10 10 10 −3

ne (cm )

Fig. 8. In case of pure photoionized plasmas (i.e. RR dominant at low temperature and DR dominant at high temperature), ratio R (=z/(x+y)) is reported as a function of ne for C v, N vi, O vii, Ne ix, Mg xi, and Si xiii at different electronic temperatures (Te in Kelvin). For low temperatures (the two first reported here: solid curves and dot-dashed curves), the value of R is independent of the value of Xion . As the temperature increases, Xion is high enough to maintain recombination dominant compared to collisional excitation from the ground level: ∼ 102 and 103−4 (for increasing temperature: respectively for long-dashed curves and short-dashed curves).


Xion=100 Xion=10000 photoionized C V Xion=1 hybrid

16 14 12

4.0

15

Ne IX

Xion=10 Xion=1000

3.5

Xion=0.1

collisional

3.0

Xion=1.55e−3

2.5

10

Xion=2.57e−2

R

R

8

2.0

6

1.5 1.0

4 5

T=4.10 K

2 0 5 10

6

7

10

6

T=2.10 K

0.5 8

10

9

10

10

10

11

10

−3

10

0.0 8 10

12

10

9

10

10

Xion=100

6

Xion=10000

N VI

Xion=1

3.5 3.0

5

10

12

10 −3

13

10

14

10

15

10

ne ( cm )

ne (cm ) 7

11

10

Xion=3.16e−3

2.5

Mg XI

Xion=1000 Xion=10 Xion=0.1 Xion=1.86e−2

4

R

R 2.0 3

1.5

2 1

1.0 5

0.5

T=6.3 10 K

0 6 10

7

10

8

10

9

10

10

11

10

12

10

−3

10

0.0 9 10

13

10

6

T=3.2.10 K 10

10

11

10

ne (cm )

12

10

13

10 −3

14

10

15

10

16

10

ne (cm )

5

Xion=100 Xion=10000 4

3.0

O VII

Xion=1

2.5

Xion=8.71e−3

2.0

3

R

R

Xion=1000 Xion=10 Xion=0.1

Si XIII

Xion=2.63e−2

1.5

2

1.0 1

6

0.5

T=10 K 0 6 10

7

10

8

10

9

10

10

10

−3

11

10

ne (cm )

12

10

13

10

14

10

6

T=5.10 K

0.0 9 10 11 12 13 14 15 16 17 10 10 10 10 10 10 10 10 10 −3

ne (cm )

Fig. 9. In case of hybrid plasmas (partially photoionized: recombination plus collisional excitation from the ground level), the ratio R (=z/(x+y)) is reported as a function of ne for C v, N vi, O vii, Ne ix, Mg xi, and Si xiii at different values of Xion (=H-like/He-like ionic fraction). R is calculated at the temperature corresponding to the maximum of the He-like ion abundance for a collisional plasma (see Arnaud & Rothenflug 1985). Solid curves: the lowest values of Xion corresponds to hybrid plasmas, and the highest value of Xion to pure photoionized plasmas. Long-dashed curves: Xion is equal to the ratio H-like/He-like in a case of collisional plasma (from Arnaud & Rothenflug 1985). Note: for C v, N vi and O vii at these temperatures, the curves for Xion =100 and 10 000 are indistinguishable.

16

Porquet & Dubau: Photoionized plasma diagnostics with He-like ions 16

16

Si

14

Mg

12

Z 10

Z 10

8

8

7 6

C 10

8

14 12

10

O N

4 7 10

12

Ne

8 6

14

10

9

10

6

10

10

11

10 −3

12

ne (cm )

10

13

10

14

10

15

4

10

5

10

6

10

7

Te (K)

Fig. 10. At left: This figure reports for each ion treated in this paper the two decades (approximatively) where the ratio R is strongly sensitive to the density. At right: the approximative range of temperatures for each ion where the plasma can be considered purely photoionized, independent of the Xion value.


0.8

0.8

ne= 10 10

0.7

0.6

w

z

0.5

arbitrary units

arbitrary units

0.7

0.4 0.3

x+y

0.2

z

0.5 0.4

x+y w

0.3

560

565

570

575

0.0 555

580

560

Energy (eV)

565

570

575

580

Energy (eV)

0.8

0.8

ne=10

11

0.7

0.6

w

0.5 0.4 0.3

z

arbitrary units

arbitrary units

10

0.1

0.0 555

x+y

0.5 0.4

0.1

0.1 565

570

575

0.0 555

580

z

w 560

Energy (eV)

ne=10

12

0.7

arbitrary units

x+y w

0.5 0.4 0.3

0.1 0.0 555

570

Energy (eV)

580

575

580

ne=10

12

0.5 0.4

w

0.3

0.1 565

575

0.6

0.2

z 560

570

x+y

0.8

0.6

0.2

565

Energy (eV)

0.8 0.7

11

x+y

0.3 0.2

560

ne=10

0.6

0.2

0.0 555

arbitrary units

ne=10

0.6

0.2

0.1

0.7

17

0.0 555

z 560

565

570

575

580

Energy (eV)

Fig. 11. O vii theoretical spectra constructed using the RGS (XMM) resolving power (E/∆E) for three values of density (in cm−3 ). This corresponds (approximatively) to the range where the ratio R is very sensitive to density. z: forbidden lines, x+y: intercombination lines and w: resonance line. At left: “hybrid plasma” at Te =1.5 106 K and Xion =1; At right: “pure” photoionized plasma at Te =105 K (at this temperature this part of the spectra are independent of the value of Xion , see Figure 7). Note: the intensities are normalized in order to have the sum of the lines equal to the unity.

18


Table 1. Energy (in cm−1 ) for the first 17 levels for C v, N vi, O vii, Ne ix, Mg xi and Si xiii calculated by the SUPERSTRUCTURE code (except for the first seven levels which are from Vainshtein & Safronova 1985). Here X(Y) means X×10Y . i

conf

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1s2 1s 2s 1s 2p 1s 2p 1s 2p 1s 2s 1s 2p 1s 3s 1s 3p 1s 3p 1s 3p 1s 3s 1s 3d 1s 3d 1s 3d 1s 3d 1s 3p

level 1

S0 3 S1 3 P0 3 P1 3 P2 1 S0 1 P1 3 S1 3 P0 3 P1 3 P2 1 S0 3 D1 3 D2 3 D3 1 D2 1 P1

Cv

N vi

O vii

Ne ix

Mg xi

Si xiii

0. 2.4114 (+6) 2.4553 (+6) 2.4552 (+6) 2.4554 (+6) 2.4551 (+6) 2.4833 (+6) 2.8239 (+6) 2.8352 (+6) 2.8352 (+6) 2.8353 (+6) 2.8401 (+6) 2.8408 (+6) 2.8408 (+6) 2.8408 (+6) 2.8411 (+6) 2.8433 (+6)

0. 3.3859 (+6) 3.4383 (+6) 3.4383 (+6) 3.4386 (+6) 3.4393 (+6) 3.4737 (+6) 3.9765 (+6) 3.9902 (+6) 3.9903 (+6) 3.9904 (+6) 3.9953 (+6) 3.9973 (+6) 3.9973 (+6) 3.9973 (+6) 3.9977 (+6) 4.0004 (+6)

0. 4.5253 (+6) 4.5863 (+6) 4.5863 (+6) 4.5869 (+6) 4.5884 (+6) 4.6291 (+6) 5.3251 (+6) 5.3441 (+6) 5.3412 (+6) 5.3414 (+6) 5.3463 (+6) 5.3497 (+6) 5.3497 (+6) 5.3498 (+6) 5.3502 (+6) 5.3534 (+6)

0. 7.2996 (+6) 7.3779 (+6) 7.3782 (+6) 7.3798 (+6) 7.3824 (+6) 7.4361 (+6) 8.6105 (+6) 8.6314 (+6) 8.6316 (+6) 8.6322 (+6) 8.6368 (+6) 8.6433 (+6) 8.6433 (+6) 8.6435 (+6) 8.6411 (+6) 8.6480 (+6)

0. 10.7358 (+6) 10.8317 (+6) 10.8325 (+6) 10.8361 (+6) 10.8385 (+6) 10.9062 (+6) 12.6824 (+6) 12.7081 (+6) 12.7087 (+6) 12.7099 (+6) 12.7136 (+6) 12.7238 (+6) 12.7239 (+6) 12.7244 (+6) 12.7251 (+6) 12.7294 (+6)

0. 14.8357 (+6) 14.9495 (+6) 14.9513 (+6) 14.9585 (+6) 14.9585 (+6) 15.0417 (+6) 17.5435 (+6) 17.5741 (+6) 17.5752 (+6) 17.5775 (+6) 17.5795 (+6) 17.5942 (+6) 17.5945 (+6) 17.5953 (+6) 17.5962 (+6) 17.6005 (+6)

Table 2. Radiative transitions probabilities (Aki in s−1 , i=1,7; k=2,17) for C v, N vi, O vii, Ne ix, Mg xi and Si xiii calculated by the SUPERSTRUCTURE code, except for marked values (a) which are from Lin et al. (1977) and (b) which are from Mewe & Schrijver (1978a). i and k correspond respectively to the lower and the upper level of the transition. Aki (s−1 ) i

k

Cv

N vi

O vii

Ne ix

Mg xi

Si xiii

1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 4 4 4 4 5 5 5 5 5 6 6 6 7 7 7 7

2 4 5 6 7 10 17 3 4 5 9 10 11 17 8 13 8 13 14 16 8 13 14 15 16 7 10 17 12 13 14 16

4.960 (+01)a 2.159 (+07) 2.650 (+04)a 3.310 (+05)a 9.477 (+11) 6.939 (+06) 3.105 (+11) 5.616 (+07) 5.655 (+07) 5.735 (+07) 1.376 (+10) 1.375 (+10) 1.374 (+10) 2.898 (+05) 7.088 (+08) 2.349 (+10) 2.129 (+09) 1.761 (+10) 3.165 (+10) 5.150 (+07) 3.557 (+09) 1.174 (+09) 1.054 (+10) 4.225 (+10) 2.214 (+07) 5.875 (+06) 4.013 (+05) 1.457 (+10) 5.646 (+09) 3.673 (+05) 6.862 (+07) 3.950 (+10)

2.530 (+02)b 1.100 (+08) 1.030 (+05)b 9.430 (+05)b 1.911 (+12) 3.525 (+07) 6.061 (+11) 6.717 (+07) 6.794 (+07) 6.955 (+07) 2.872 (+10) 2.870 (+10) 2.867 (+10) 1.607 (+06) 1.366 (+09) 4.847 (+10) 4.106 (+09) 3.634 (+10) 6.519 (+10) 2.346 (+08) 6.870 (+09) 2.421 (+09) 2.169 (+10) 8.718 (+10) 1.025 (+08) 9.199 (+06) 2.088 (+06) 2.982 (+10) 1.145 (+10) 1.940 (+06) 3.164 (+08) 8.194 (+10)

1.060 (+03)a 4.447 (+08) 3.330 (+05)a 2.310 (+06)a 3.467 (+12) 1.423 (+08) 1.073 (+12) 7.818 (+07) 7.956 (+07) 8.249 (+07) 5.342 (+10) 5.337 (+10) 5.329 (+10) 6.902 (+06) 2.398 (+09) 8.947 (+10) 7.211 (+09) 6.706 (+10) 1.199 (+11) 8.525 (+08) 1.208(+10) 4.468(+09) 3.983(+10) 1.609(+11) 3.784(+08) 1.307 (+07) 8.582 (+06) 5.478 (+10) 2.071 (+10) 8.054 (+06) 1.162 (+09) 1.516 (+11)

1.100 (+04)a 4.470 (+09) 2.270 (+06)a 1.000 (+07)a 9.197 (+12) 1.429 (+09) 2.752 (+12) 1.003 (+08) 1.039 (+08) 1.118 (+08) 1.466 (+11) 1.464 (+11) 1.461 (+11) 7.514 (+07) 6.079 (+09) 2.432 (+11) 1.831 (+10) 1.822 (+11) 3.213 (+11) 6.862 (+09) 3.080(+10) 1.213(+10) 1.061(+11) 4.369(+11) 3.145(+09) 2.266 (+07) 8.838 (+07) 1.482 (+11) 5.436 (+10) 8.401 (+07) 9.519 (+09) 4.092 (+11)

7.330 (+04)a 2.867(+10) 1.060 (+07)a 3.220 (+07)a 2.010 (+13) 9.141 (+09) 5.877 (+12) 1.228 (+08) 1.304 (+08) 1.486 (+08) 3.280 (+11) 3.269 (+11) 3.262 (+11) 5.061 (+08) 1.290 (+10) 5.408 (+11) 3.890 (+10) 4.046 (+11) 6.967 (+11) 3.311 (+10) 6.583(+10) 2.695(+10) 2.268(+11) 9.708(+11) 1.582(+10) 3.541 (+07) 5.759 (+08) 3.286 (+11) 1.175 (+11) 5.522 (+08) 4.675 (+10) 8.896 (+11)

3.610 (+05)a 1.345 (+11) 3.890 (+07)a 8.470 (+07)a 3.857 (+13) 4.268 (+10) 1.107 (+13) 1.460 (+08) 1.602 (+08) 1.977 (+08) 6.406 (+11) 6.366 (+11) 6.360 (+11) 2.452 (+09) 2.426 (+10) 1.052 (+12) 7.315 (+10) 7.856 (+11) 1.314 (+12) 1.073 (+11) 1.248(+11) 5.240(+10) 4.173(+11) 1.887(+12) 5.438(+10) 5.286 (+07) 2.730 (+09) 6.371 (+11) 2.232 (+11) 2.638 (+09) 1.547 (+11) 1.674 (+12)


19

Table 3. Radiative and dielectronic recombination rates (respectively RR and DR) calculated in this work (in cm3 s−1 ) for each n=2 level of C v. Te 5.0 (+04)

1.0 (+05) 2.0 (+05) 5.0 (+05) 1.0 (+06) 2.0 (+06)

a b c

3 S1 2.43 (-13)a 8.97 (-13)b 0c 1.71 (-13) 5.78 (-13) 0 1.20 (-13) 3.58 (-13) 4.32 (-19) 7.35 (-14) 1.75 (-13) 2.75 (-15) 4.96 (-14) 9.64 (-14) 3.72 (-14) 3.24 (-14) 4.98 (-14) 8.57 (-14)

3 P0 7.13 (-14) 2.51 (-13) 0 4.85 (-14) 1.43 (-13) 0 3.20 (-14) 7.80 (-14) 1.34 (-20) 1.71 (-14) 3.19 (-14) 4.72 (-16) 9.77 (-15) 1.53 (-14) 8.94 (-15) 5.10 (-15) 7.10 (-15) 2.32 (-14)

3 P1 2.14 (-13) 7.51 (-13) 0 1.46 (-13) 4.30 (-13) 0 9.60 (-14) 2.34 (-13) 3.81 (-20) 5.12 (-14) 9.58 (-14) 1.28 (-15) 2.93 (-14) 4.60 (-14) 2.42 (-14) 1.53 (-14) 2.12 (-14) 6.26 (-14)

3 P2 3.57 (-13) 1.25 (-12) 0 2.43 (-13) 7.16 (-13) 0 1.60 (-13) 3.89 (-13) 5.13 (-20) 8.54 (-14) 1.60 (-13) 1.55 (-15) 4.89 (-14) 7.61 (-14) 2.85 (-14) 2.55 (-14) 3.53 (-14) 7.31 (-14)

1 S0 8.09 (-14) 1.69 (-14) 0 5.69 (-14) 1.09 (-14) 0 3.99 (-14) 6.70 (-15) 1.33 (-19) 2.45 (-14) 3.30 (-15) 6.77 (-16) 1.65 (-14) 1.80 (-15) 8.17 (-15) 1.08 (-14) 9.00 (-16) 1.80 (-14)

1 P1 2.14 (-13) 6.87 (-13) 0 1.46 (-13) 3.89 (-13) 0 9.60 (-14) 2.09 (-13) 5.61(-19) 5.12 (-14) 8.38 (-14) 4.56 (-15) 2.93 (-14) 3.95 (-14) 6.92 (-14) 1.53 (-14) 1.79 (-14) 1.68 (-13)

RR direct contribution. RR upper level radiative cascade contribution from the n>2 levels. DR direct plus upper level radiative cascade from the n>2 levels contributions (when the value is equal to zero this means that the DR rate is negligible compared to the RR rates).

Note: a+b+c represent the total recombination rates.

Table 4. Same as Table 4 for N vi. Te 7.0 (+04) 1.4 (+05) 2.8 (+05) 7.0 (+05) 1.4 (+06) 2.8 (+06)

3 S1 2.86 (-13) 1.07 (-12) 0 2.02 (-13) 6.91 (-13) 0 1.41 (-13) 4.28 (-13) 8.56 (-18) 8.68 (-14) 2.10 (-13) 6.58 (-15) 5.86 (-14) 1.15 (-13) 4.88 (-14) 3.82 (-14) 5.97 (-14) 9.17 (-14)

3 P0 8.42 (-14) 2.94 (-13) 0 5.73 (-14) 1.68 (-13) 0 3.78 (-14) 9.12 (-14) 3.67 (-20) 2.02 (-14) 3.72 (-14) 5.98 (-16) 1.15 (-14) 1.79 (-14) 1.03 (-14) 6.02 (-15) 8.18 (-15) 2.56 (-14)

3 P1 2.53 (-13) 8.77 (-13) 0 1.72 (-13) 5.04 (-13) 0 1.13 (-13) 2.74 (-13) 1.34 (-19) 6.05 (-14) 1.12 (-13) 1.50 (-15) 3.46 (-14) 5.36 (-14) 2.54 (-14) 1.81 (-14) 2.46 (-14) 6.27 (-14)

3 P2 4.21 (-13) 1.47 (-12) 0 2.86 (-13) 8.44 (-13) 0 1.89 (-13) 4.56 (-13) 2.38 (-19) 1.01 (-13) 1.86 (-13) 1.75 (-15) 5.76 (-14) 8.94 (-14) 2.82 (-14) 3.01 (-14) 4.11 (-14) 6.85 (-14)

1 S0 9.55 (-14) 2.35 (-14) 0 6.72 (-14) 1.52 (-14) 0 4.71 (-14) 9.30 (-15) 2.90 (-18) 2.89 (-14) 4.60 (-15) 2.00 (-15) 1.95 (-14) 2.50 (-15) 1.26 (-14) 1.27 (-14) 1.30 (-15) 2.16 (-14)

1 P1 2.53 (-13) 8.07 (-13) 0 1.72 (-13) 4.58 (-13) 0 1.13 (-13) 2.46 (-13) 1.17 (-17) 6.05 (-14) 9.85 (-14) 9.76 (-15) 3.46 (-14) 4.64 (-14) 8.57 (-14) 1.81 (-14) 2.09 (-14) 1.76 (-13)

20


Table 5. Same as Table 4 for O vii. Te 9.0 (+04) 1.8 (+05) 3.6 (+05) 9.0 (+05) 1.8 (+06) 3.6 (+06)

3 S1 3.36 (-13) 1.24 (-12) 0 2.37 (-13) 8.03 (-13) 0 1.66 (-13) 4.95 (-13) 9.67 (-19) 1.02 (-13) 2.44 (-13) 3.55 (-15) 6.90 (-14) 1.34 (-13) 3.90 (-14) 4.51 (-14) 6.99 (-14) 8.19 (-14)

3 P0 9.90 (-14) 3.51 (-13) 0 6.74 (-14) 2.02 (-13) 0 4.45 (-14) 1.10 (-13) 1.86 (-20) 2.39 (-14) 4.52 (-14) 4.90(-16) 1.37 (-14) 2.18 (-14) 8.49 (-15) 7.19 (-15) 1.00 (-14) 2.11 (-14)

3 P1 2.97 (-13) 1.05 (-12) 0 2.02 (-13) 6.05 (-13) 0 1.34 (-13) 3.29 (-13) 5.19 (-20) 7.16 (-14) 1.35 (-13) 1.32 (-15) 4.11 (-14) 6.49 (-14) 2.26 (-14) 2.16 (-14) 3.01 (-14) 5.60 (-14)

3 P2 4.95 (-13) 1.75 (-12) 0 3.37 (-13) 1.01 (-12) 0 2.23 (-13) 5.50 (-13) 6.73 (-20) 1.19 (-13) 2.27 (-13) 1.54 (-15) 6.85 (-14) 1.09 (-13) 2.57 (-14) 3.60 (-14) 5.02 (-14) 6.28 (-14)

1 S0 1.12 (-13) 2.50 (-14) 0 7.89 (-14) 1.63 (-14) 0 5.53 (-14) 1.01 (-14) 3.42 (-19) 3.40 (-14) 4.90 (-15) 1.05 (-15) 2.30 (-14) 2.70 (-15) 1.01 (-14) 1.50 (-14) 1.40 (-15) 1.98 (-14)

1 P1 2.97 (-13) 9.63 (-13) 0 2.02 (-13) 5.50 (-13) 0 1.34 (-13) 2.96 (-13) 1.36 (-18) 7.16 (-14) 1.19 (-13) 6.02 (-15) 4.11 (-14) 5.65 (-14) 7.43 (-14) 2.16 (-14) 2.56 (-14) 1.65 (-13)

3 P0 1.27 (-13) 4.57 (-13) 0 8.69 (-14) 2.62 (-13) 0 5.75 (-14) 1.43 (-13) 1.19 (-20) 3.09 (-14) 5.93 (-14) 2.68 (-16) 1.78 (-14) 2.86 (-14) 4.47 (-15) 9.39 (-15) 1.32 (-14) 1.09 (-14)

3 P1 3.82 (-13) 1.37 (-12) 0 2.61 (-13) 7.89 (-13) 0 1.73 (-13) 4.31 (-13) 3.74 (-20) 9.28 (-14) 1.78 (-13) 8.31 (-16) 5.35 (-14) 8.55 (-14) 1.38 (-14) 2.82 (-14) 3.96 (-14) 3.37 (-14)

3 P2 6.37 (-13) 2.28 (-12) 0 4.35 (-13) 1.31 (-12) 0 2.88 (-13) 7.22 (-13) 5.73 (-20) 1.55 (-13) 2.97 (-13) 1.19 (-15) 8.91 (-14) 1.43 (-13) 1.96 (-14) 4.70 (-14) 6.60 (-14) 4.75 (-14)

1 S0 1.44 (-13) 3.40 (-14) 0 1.02 (-13) 2.20 (-14) 0 7.12 (-14) 1.36 (-14) 5.29 (-19) 4.38 (-14) 6.70 (-15) 1.38 (-15) 2.97 (-14) 3.60 (-15) 1.23 (-14) 1.94 (-14) 1.90 (-15) 2.32 (-14)

1 P1 3.82 (-13) 1.26 (-12) 0 2.61 (-13) 7.19 (-13) 0 1.73 (-13) 3.88 (-13) 2.01 (-18) 9.28 (-14) 1.57 (-13) 6.78 (-15) 5.35 (-14) 7.45 (-14) 7.45 (-14) 2.82 (-14) 3.40 (-14) 1.57 (-13)

3 P0 1.56 (-13) 5.65 (-13) 0 1.07 (-13) 3.25 (-13) 0 7.07 (-14) 1.78 (-13) 7.95 (-21) 3.81 (-14) 7.39 (-14) 1.71 (-16) 2.21 (-14) 3.56 (-14) 2.83 (-15) 1.17 (-14) 1.64 (-14) 6.90( -15)

3 P1 4.69 (-13) 1.70 (-12) 0 3.20 (-13) 9.80 (-13) 0 2.12 (-13) 5.36 (-13) 2.92 (-20) 1.14 (-13) 2.22 (-13) 6.40 (-16) 6.62 (-14) 1.07 (-13) 1.07 (-14) 3.50 (-14) 4.95 (-14) 2.62 (-14)

3 P2 7.82 (-13) 2.83 (-12) 0 5.34 (-13) 1.63 (-12) 0 3.54 (-13) 8.96 (-13) 4.91 (-20) 1.91 (-13) 3.70 (-13) 9.60 (-16) 1.10 (-13) 1.79 (-13) 1.59 (-14) 5.83 (-14) 8.27 (-14) 3.88 (-14)

1 S0 1.77 (-13) 4.30 (-14) 0 1.25 (-13) 2.80 (-14) 0 8.74 (-14) 1.76 (-14) 6.68 (-19) 5.38 (-14) 8.60 (-15) 1.61 (-15) 3.64 (-14) 4.80 (-15) 1.36 (-14) 2.39 (-14) 2.50 (-15) 2.47 (-14)

1 P1 4.69 (-13) 1.56 (-12) 0 3.20 (-13) 8.90 (-13) 0 2.12 (-13) 4.85 (-13) 2.45 (-18) 1.14 (-13) 1.98 (-13) 7.10 (-15) 6.62 (-14) 9.38 (-14) 7.11 (-14) 3.50 (-14) 4.27 (-14) 1.44 (-13)

Table 6. Same as Table 4 for Ne ix. Te 1.4 (+05) 2.8 (+05) 5.6 (+05) 1.4 (+06) 2.8 (+06) 5.6 (+06)

3 S1 4.33 (-13) 1.59 (-12) 0 3.05 (-13) 1.02 (-12) 0 2.14 (-13) 6.35 (-13) 1.22 (-18) 1.31 (-13) 3.15 (-13) 3.65 (-15) 8.90 (-14) 1.73 (-13) 3.66 (-14) 5.83 (-14) 8.97 (-14) 7.37 (-14)

Table 7. Same as Table 4 for Mg xi. Te 2.0 (+05) 4.0 (+05) 8.0 (+05) 2.0 (+06) 4.0 (+06) 8.0 (+06)

3 S1 5.30 (-13) 1.94 (-12) 0 3.74 (-13) 1.25 (-12) 0 2.62 (-13) 7.78 (-13) 1.19 (-18) 1.61 (-13) 3.85 (-13) 3.36 (-15) 1.09 (-13) 2.13 (-13) 3.31 (-14) 7.17 (-14) 1.11 (-13) 6.62 (-14)


21

Table 8. Same as Table 4 for Si xiii. Te 2.8 (+05) 5.5 (+05) 1.1 (+06) 2.8 (+06) 5.5 (+06) 1.1(+07)

3 S1 6.23 (-13) 2.25 (-12) 0 4.39 (-13) 1.44 (-12) 0 3.08 (-13) 8.92 (-13) 1.29 (-18) 1.90 (-13) 4.45 (-13) 3.43 (-15) 1.29 (-13) 2.46 (-13) 2.97 (-14) 8.43 (-14) 1.29 (-13) 5.84 (-14)

3 P0 1.84 (-13) 6.65 (-13) 0 1.25 (-13) 3.84 (-13) 0 8.32 (-14) 2.10 (-13) 8.47 (-21) 4.49 (-14) 8.71 (-14) 1.77 (-16) 2.59 (-14) 4.20 (-14) 2.50 (-15) 1.37 (-14) 1.94 (-14) 5.93 (-15)

3 P1 5.52 (-13) 2.00 (-12) 0 3.76 (-13) 1.15 (-12) 0 2.49 (-13) 6.32 (-13) 3.32 (-20) 1.35 (-13) 2.61 (-13) 6.55 (-16) 7.78 (-14) 1.26 (-13) 9.28 (-15) 4.12 (-14) 5.83 (-14) 2.21 (-14)

3 P2 9.19 (-13) 3.33 (-12) 0 6.27 (-13) 1.92 (-12) 0 4.16 (-13) 1.05 (-12) 6.78 (-20) 2.24 (-13) 4.37 (-13) 9.75 (-16) 1.30 (-13) 2.11 (-13) 1.35 (-14) 6.86 (-14) 9.74 (-14) 3.20 (-14)

1 S0 2.08 (-13) 5.30 (-14) 0 1.46 (-13) 3.50 (-14) 0 1.03 (-13) 2.10 (-14) 9.70 (-19) 6.32 (-14) 1.06 (-14) 2.09 (-15 ) 4.28 (-14) 5.90 (-15) 1.48 (-14) 2.81 (-14) 3.10 (-15) 2.55 (-14)

1 P1 5.52 (-13) 1.85 (-12) 0 3.76 (-13) 1.05 (-12) 0 2.49 (-13) 5.74 (-13) 3.46 (-18) 1.35 (-13) 2.34 (-13) 8.56 (-15) 7.78 (-14) 1.11 (-13) 6.93 (-14) 4.12 (-14) 5.07 (-14) 1.30 (-13)

Table 9. Effective collisions strengths (Υ) for each 1s2 –1s2l transition of C v. Te /Z 3 400 600 900 1 350 2 000 3 000 4 500 6 700 10 000

a

b

3 S1 8.48 (-03)a 7.53 (-06)b 9.09 (-03) 8.96 (-05) 9.46 (-03) 4.76 (-04) 9.39 (-03) 1.45 (-03) 8.91 (-03) 2.97 (-03) 8.14 (-03) 4.75 (-03) 7.23 (-03) 6.23 (-03) 6.30 (-03) 7.08 (-03) 5.37 (-03) 7.23 (-03)

3 P0 4.95 (-03) 7.67 (-07) 5.04 (-03) 6.94 (-06) 5.02 (-03) 3.12 (-05) 4.85 (-03) 8.59 (-05) 4.56 (-03) 1.64 (-04) 4.15 (-03) 2.51 (-04) 3.68 (-03) 3.20 (-04) 3.20 (-03) 3.56 (-04) 2.70 (-03) 3.59 (-04)

3 P1 1.48 (-02) 2.31 (-06) 1.51 (-02) 2.09 (-05) 1.50 (-02) 9.37 (-05) 1.46 (-02) 2.58 (-04) 1.37 (-02) 4.93 (-04) 1.25 (-02) 7.54 (-04) 1.11 (-02) 9.60 (-04) 9.60 (-03) 1.07 (-03) 8.09 (-03) 1.08 (-03)

3 P2 2.47 (-02) 3.88 (-06) 2.51 (-02) 3.50 (-05) 2.51 (-02) 1.57 (-04) 2.42 (-02) 4.32 (-04) 2.27 (-02) 8.26 (-04) 2.08 (-02) 1.26 (-03) 1.84 (-02) 1.61 (-03) 1.60 (-02) 1.79 (-03) 1.34 (-02) 1.80 (-03)

1 S0 1.42 (-02) 4.32 (-07) 1.46 (-02) 4.40 (-06) 1.50 (-02) 2.28 (-05) 1.52 (-02) 7.53 (-05) 1.55 (-02) 1.80 (-04) 1.58 (-02) 3.62 (-04) 1.62 (-02) 6.36 (-04) 1.68 (-02) 1.01 (-03) 1.76 (-02) 1.50 (-03)

1 P1 4.05 (-02) 9.86 (-06) 4.26 (-02) 7.09 (-05) 4.48 (-02) 2.73 (-04) 4.76 (-02) 6.95 (-04) 5.13 (-02) 1.31 (-03) 5.65 (-02) 2.10 (-03) 6.40 (-02) 2.97 (-03) 7.38 (-02) 3.88 (-03) 8.70 (-02) 4.82 (-03)

direct + resonance contribution inferred from the data for O vii (from Zhang & Sampson 1987, see Table 10) with the scaling reported in Figure 4 . cascade contribution calculated in this paper. Note: here a+b corresponds to the total collision strength which populates the level considered.

22


Table 10. Effective collisions strengths (Υ) for each 1s2 –1s2l transition of O vii. Te /Z 3 400 600 900 1350 2000 3000 4500 6 700 10 000

a b c

3 S1 4.06 (-03)a 5.01 (-04)b 1.82 (-05)c 4.06 (-03) 8.27 (-04) 1.33 (-04) 4.04 (-03) 1.05 (-03) 5.05 (-04) 3.96 (-03) 1.09 (-03) 1.22 (-03) 3.80 (-03) 9.86 (-04) 2.14 (-03) 3.58 (-03) 8.04 (-04) 3.04 (-03) 3.28 (-03) 6.09 (-04) 3.67 (-03) 2.94 (-03) 4.51 (-04) 3.91 (-03) 2.57 (-03) 3.16 (-04) 3.81 (-03)

3 P0 2.51 (-03) 1.53 (-04) 1.32 (-06) 2.48 (-03) 2.31 (-04) 8.38 (-06) 2.42 (-03) 2.75 (-04) 2.94 (-05) 2.33 (-03) 2.74 (-04) 6.80 (-05) 2.21 (-03) 2.42 (-04) 1.15 (-04) 2.04 (-03) 1.93 (-04) 1.60 (-04) 1.83 (-03) 1.45 (-04) 1.90 (-04) 1.61 (-03) 1.06 (-04) 2.01 (-04) 1.37 (-03) 7.53 (-05) 1.94 (-04)

3 P1 7.50 (-03) 4.60 (-04) 3.95 (-06) 7.41 (-03) 6.97 (-04) 2.51 (-05) 7.26 (-03) 8.31 (-04) 8.82 (-05) 7.00 (-03) 8.29 (-04) 2.04 (-04) 6.63 (-03) 7.31 (-04) 3.45 (-04) 6.12 (-03) 5.86 (-04) 4.81 (-04) 5.51 (-03) 4.42 (-04) 5.72 (-04) 4.84 (-03) 3.22 (-04) 6.04 (-04) 4.12 (-03) 2.28 (-04) 5.85 (-04)

3 P2 1.25 (-02) 7.71 (-04) 6.67 (-06) 1.23 (-02) 1.16 (-03) 4.23 (-05) 1.21 (-02) 1.38 (-03) 1.48 (-04) 1.16 (-02) 1.37 (-03) 3.42 (-04) 1.10 (-02) 1.20 (-03) 5.79 (-04) 1.02 (-02) 9.73 (-04) 8.06 (-04) 9.18 (-03) 7.32 (-04) 9.57 (-04) 8.06 (-03) 5.33 (-04) 1.01 (-03) 6.85 (-03) 3.76 (-04) 9.77 (-04)

1 S0 7.35 (-03) 2.92 (-04) 9.42 (-07) 7.45 (-03) 4.06 (-04) 6.68 (-06) 7.59 (-03) 4.56 (-04) 2.71 (-05) 7.75 (-03) 4.38 (-04) 7.61 (-05) 7.94 (-03) 3.78 (-04) 1.63 (-04) 6.26 (-03) 2.28 (-04) 3.04 (-04) 8.51 (-03) 2.23 (-04) 5.05 (-04) 8.89 (-03) 1.61 (-04) 7.70 (-04) 9.34 (-03) 1.14 (-04) 1.11 (-03)

1 P1 2.10 (-02) 7.53 (-04) 1.26 (-05) 2.19 (-02) 9.84 (-04) 6.98 (-05) 2.30 (-02) 1.06 (-03) 2.26 (-04) 2.46 (-02) 9.83 (-04) 5.12 (-04) 2.68 (-02) 8.31 (-04) 8.96 (-04) 2.97 (-02) 6.47 (-04) 1.37 (-03) 3.39 (-02) 4.81 (-04) 1.88 (-03) 3.93 (-02) 3.45 (-04) 2.41 (-03) 4.65 (-02) 2.42 (-04) 2.96 (-03)

direct contribution (from Zhang & Sampson 1987). resonance contribution (from Zhang & Sampson 1987). cascade contribution calculated in this paper. Note: here a+b+c corresponds to the total collision strength which populates the level considered.

Table 11. Same as Table 10 but for the Ne ix. Te /Z 3 400 600 900 1350 2000 3000 4500 6700 10000

3

S1 2.53 (-03) 5.05 (-04) 3.14 (-05) 2.53 (-03) 6.75 (-04) 1.64 (-04) 2.50 (-03) 7.34 (-04) 4.96 (-04) 2.43 (-03) 6.89 (-04) 1.03 (-03) 2.31 (-03) 5.78 (-04) 1.60 (-03) 2.15 (-03) 4.49 (-04) 2.10 (-03) 1.95 (-03) 3.30 (-04) 2.39 (-03) 1.72 (-03) 2.36 (-04) 2.43 (-03) 1.49 (-03) 1.64 (-04) 2.29 (-03)

3

P0 1.56 (-03) 1.41 (-04) 1.97 (-06) 1.53 (-03) 1.77 (-04) 9.55 (-06) 1.49 (-03) 1.85 (-04) 2.77 (-05) 1.42 (-03) 1.69 (-04) 5.59 (-05) 1.33 (-03) 1.40 (-04) 8.61 (-05) 1.21 (-03) 1.08 (-04) 1.11 (-04) 1.08 (-03) 7.91 (-05) 1.25 (-04) 9.32 (-04) 5.65 (-05) 1.27 (-04) 7.83 (-04) 3.93 (-05) 1.19 (-04)

3

P1 4.67 (-03) 4.23 (-04) 5.91 (-06) 4.59 (-03) 5.35 (-04) 2.87 (-05) 4.47 (-03) 5.62 (-04) 8.32 (-05) 4.27 (-03) 5.11 (-04) 1.68 (-04) 4.00 (-03) 4.25 (-04) 2.59 (-04) 3.65 (-03) 3.26 (-04) 3.35 (-04) 3.24 (-03) 2.39 (-04) 3.78 (-04) 2.81 (-03) 1.70 (-04) 3.85 (-04) 2.36 (-03) 1.19 (-04) 3.62 (-04)

3

P2 7.77 (-03) 7.04 (-04) 9.99 (-06) 7.65 (-03) 8.89 (-04) 4.84 (-05) 7.43 (-03) 9.29 (-04) 1.40 (-04) 7.10 (-03) 8.44 (-04) 2.83 (-04) 6.64 (-03) 6.96 (-04) 4.35 (-04) 6.06 (-03) 5.37 (-04) 5.63 (-04) 5.39 (-03) 3.94 (-04) 6.33 (-04) 4.66 (-03) 2.80 (-04) 6.42 (-04) 3.91 (-03) 1.97 (-04) 6.01 (-04)

1

S0 4.79 (-03) 2.44 (-04) 1.63 (-06) 4.88 (-03) 2.93 (-04) 8.87 (-06) 4.96 (-03) 2.95 (-04) 3.02 (-05) 5.08 (-03) 2.62 (-04) 7.49 (-05) 5.21 (-03) 2.14 (-04) 1.48 (-04) 5.39 (-03) 1.63 (-04) 2.61 (-04) 5.61 (-03) 1.19 (-04) 4.17 (-04) 5.86 (-03) 8.50 (-05) 6.18 (-04) 6.17 (-03) 5.92 (-05) 8.73 (-04)

1

P1 1.45 (-02) 5.92 (-04) 1.64 (-05) 1.51 (-02) 6.76 (-04) 7.27 (-05) 1.59 (-02) 6.63 (-04) 2.03 (-04) 1.71 (-02) 5.78 (-04) 4.15 (-04) 1.87 (-02) 4.67 (-04) 6.83 (-04) 2.09 (-02) 3.52 (-04) 9.97 (-04) 2.40 (-02) 2.56 (-04) 1.34 (-03) 2.80 (-02) 1.81 (-04) 1.68 (-03) 3.32 (-02) 1.26 (-04) 2.05 (-03)


Table 12. Same as Table 10 but for the Mg xi. Te /Z 3 400 600 900 1350 2000 3000 4500 6700 10000

3 S1 1.74 (-03) 4.41 (-04) 4.40 (-05) 1.72 (-03) 5.17 (-04) 1.81 (-04) 1.69 (-03) 5.11 (-04) 4.65 (-04) 1.63 (-03) 4.45 (-04) 8.56 (-04) 1.53 (-03) 3.60 (-04) 1.24 (-03) 1.41 (-03) 2.70 (-04) 1.52 (-03) 1.27 (-03) 1.94 (-04) 1.65 (-03) 1.11 (-03) 1.37 (-04) 1.63 (-03) 9.45 (-04) 9.47 (-05) 1.49 (-03)

3 P0 1.05 (-03) 1.16 -04) 2.59 (-06) 1.04 (-03) 1.32 (-04) 1.02 (-05) 1.00 (-03) 1.28 (-04) 2.56 (-05) 9.50 (-04) 1.10 (-04) 4.66 (-05) 8.77 (-04) 8.75 (-05) 6.66 (-05) 7.92 (-04) 6.57 (-05) 8.15 (-05) 6.96 (-04) 4.72 (-05) 8.78 (-05) 5.95 (-04) 3.33 (-05) 8.60 (-05) 4.93 (-04) 2.31 (-05) 7.83 (-05)

3 P1 3.18 (-03) 3.51 (-04) 7.75 (-06) 3.11 (-03) 3.97 (-04) 3.06 (-05) 3.01 (-03) 3.84 (-04) 7.68 (-05) 2.85 (-03) 3.30 (-04) 1.40 (-04) 2.65 (-03) 2.63 (-04) 2.01 (-04) 2.40 (-03) 1.85 (-04) 2.47 (-04) 2.11 (-03) 1.42 (-04) 2.68 (-04) 1.81 (-03) 9.97 (-05) 2.66 (-04) 1.51 (-03) 6.91 (-05) 2.46 (-04)

3 P2 5.28 (-03) 5.86 (-04) 1.32 (-05) 5.18 (-03) 6.61 (-04) 5.21 (-05) 5.00 (-03) 6.35 (-04) 1.30 (-04) 4.73 (-03) 5.45 (-04) 2.37 (-04) 4.38 (-03) 4.35 (-04) 3.38 (-04) 3.96 (-03) 3.25 (-04) 4.14 (-04) 3.48 (-03) 2.34 (-4) 4.47 (-04) 2.98 (-03) 1.65 (-04) 4.40 (-04) 2.47 (-03) 1.14 (-04) 4.02 (-04)

1 S0 3.39 (-03) 1.93 (-04) 2.40 (-06) 3.44 (-03) 2.10 (-04) 1.07 (-05) 3.50 (-03) 1.97 (-04) 3.19 (-05) 3.58 (-03) 1.67 (-04) 7.25 (-05) 3.69 (-03) 1.31 (-04) 1.35 (-04) 3.82 (-02) 9.77 (-05) 2.28 (-04) 3.99 (-03) 7.04 (-05) 3.54 (-04) 4.18 (-03) 4.97 (-05) 5.13 (-04) 4.39 (-03) 3.42 (-05) 7.12 (-04)

1 P1 1.06 (-02) 4.49 (-04) 2.00 (-05) 1.10 (-02) 4.74 (-04) 7.46 (-05) 1.18 (-02) 4.39 (-04) 1.85 (-04) 1.26 (-02) 3.65 (-04) 3.50 (-04) 1.39 (-02) 2.87 (-04) 5.46 (-04) 1.57 (-02) 2.12 (-04) 7.72 (-04) 1.80 (-02) 1.52 (-04) 1.01 (-03) 2.12 (-02) 1.07 (-04) 1.26 (-03) 2.51 (-02) 7.37 (-05) 1.52 (-03)

3 P1 2.31 (-03) 2.82 (-04) 9.32 (-06) 2.25 (-03) 2.95 (-04) 3.13 (-05) 2.16 (-03) 2.68 (-04) 7.01 (-05) 2.04 (-03) 2.22 (-04) 1.18 (-04) 1.88 (-03) 1.72 (-04) 1.60 (-04) 1.69 (-03) 1.27 (-04) 1.89 (-04) 1.48 (-03) 9.01 (-05) 2.00 (-04) 1.28 (-03) 6.33 (-05) 1.95 (-04) 1.07 (-03) 4.35 (-05) 1.80 (-04)

3 P2 3.81 (-03) 4.69 (-04) 1.60 (-05) 3.71 (-03) 4.88 (-04) 5.34 (-05) 3.57 (-03) 4.45 (-04) 1.19 (-04) 3.34 (-03) 3.66 (-04) 2.00 (-04) 3.08 (-03) 2.84 (-04) 2.69 (-04) 2.75 (-03) 2.09 (-04) 3.16 (-04) 2.39 (-03) 1.48 (-04) 3.30 (-04) 2.03 (-03) 1.03 (-04) 3.17 (-04) 1.66 (-03) 7.15 (-05) 2.86 (-04)

1 S0 2.51 (-03) 1.50 (-04) 3.18 (-06) 2.56 (-03) 1.52 (-04) 1.22 (-05) 2.60 (-03) 1.36 (-04) 3.28 (-05) 2.67 (-03) 1.11 (-04) 6.96 (-05) 2.75 (-03) 8.54 (-05) 1.24 (-04) 2.86 (-03) 6.26 (-05) 2.02 (-04) 2.99 (-03) 4.35 (-05) 3.06 (-04) 3.13 (-03) 3.10 (-05) 4.36 (-04) 3.29 (-03) 2.14 (-05) 5.97 (-04)

1 P1 8.07 (-03) 3.41 (-04) 2.31 (-05) 8.46 (-03) 3.39 (-04) 7.49 (-05) 9.00 (-03) 3.00 (-04) 1.69 (-04) 9.79 (-03) 2.44 (-04) 3.00 (-04) 1.08 (-02) 1.87 (-04) 4.51 (-04) 1.22 (-02) 1.36 (-04) 6.20 (-04) 1.41 (-02) 9.61 (-05) 7.98 (-04) 1.66 (-02) 6.75 (-05) 9.81 (-04) 1.99 (-02) 4.67 (-05) 1.17 (-03)

Table 13. Same as Table 10 but for the Si xiii. Te /Z 3 400 600 900 1350 2000 3000 4500 6700 10000

3 S1 1.26 (-03) 3.62 (-04) 5.44 (-05) 1.24 (-03) 3.88 (-04) 1.87 (-04) 1.21 (-03) 3.59 (-04) 4.23 (-04) 1.16 (-03) 3.01 (-04) 7.14 (-04) 1.09 (-03) 2.34 (-04) 9.68 (-04) 9.88 (-04) 1.72 (-04) 1.14 (-03) 8.78 (-04) 1.22 (-04) 1.19 (-03) 7.66 (-04) 8.54 (-05) 1.14 (-03) 6.47 (-04) 5.88 (-05) 1.02 (-03)

3 P0 7.63 (-04) 9.39 (-05) 3.11 (-06) 7.45 (-04) 9.84 (-05) 1.04 (-05) 7.13 (-04) 9.00 (-05) 2.34 (-05) 6.70 (-04) 7.44 (-05) 3.91 (-05) 6.16 (-04) 5.78 (-05) 5.27 (-05) 5.52 (-04) 4.25 (-05) 6.17 (-05) 4.80 (-04) 3.03 (-05) 6.42 (-05) 4.06 (-04) 2.12 (-05) 6.13 (-05) 3.32 (-04) 1.46 (-05) 5.46 (-05)

23

24


Table 14. Energy of the three main X-ray lines of C v, N vi, O vii, Ne ix, Mg xi and Si xiii, as well as the corresponding wavelength in ˚ A, in parentheses. w corresponds to the resonance line, x+y corresponds to the intercombination lines (here too close to be separated) and z corresponds to the forbidden line. Multiplet w x+y z

Cv 307.88 (40.27) 304.41 (40.73) 298.97 (41.47)

N vi 430.65 (28.79) 426.36 (29.08) 419.86 (29.53)

O vii 574.00 (21.60) 568.74 (21.80) 561.02 (22.10)

Ne ix 921.82 (13.45) 915.02 (13.55) 905.00 (13.70)

Mg xi 1357.07 (9.17) 1343.28 (9.23) 1331.74 (9.31)

Si xiii 1864.44 (6.65) 1853.29 (6.69) 1839.54 (6.74)